AbstractThis study provides a comprehensive empirical benchmark of quantum, classical, and Bayesian machine learning approaches for regression under challenging small-sample conditions with multicollinear features and skew-normal innovations. We systematically compare nine algorithms—including three quantum methods (Quantum Circuit Learning, Quantum Error Regression, Quantum Kernel Methods),four classical machine learning techniques (Lasso, Ridge, Random Forest, Gradient Boosting, Support Vector Regression), and Bayesian Structural Time Series— across two sample size regimes (n=30 and n=80) with five features. Outcome of the study revealed robust sample-size-dependent performance hierarchies in regularized linear methods (Lasso, Ridge) and Bayesian paradigms which ordinarily subsist in small-sample regimes of (n=30), with RMSE values of 4.46-5.74, while non-linear ensemble methods (Random Forest) exhibited superiority with moderate samples (n=80, RMSE: 2.07). Quantum machine learning methods had overtimes underperform classical benchmarks when exhibiting 91% higher error rates at small sample size of n=30, this may be due to classical method learned the noise, though Quantum Circuit Learning exhibited substantial convergence toward classical performance at n=80 (only 25% worse than best model),thus higher sample sizes thresholds will be better off for quantum-classical parity.
AbstractThis study provides a comprehensive empirical benchmark of quantum, classical, and Bayesian machine learning approaches for regression under challenging small-sample conditions with multicollinear features and skew-normal innovations. We systematically compare nine algorithms—including three quantum methods (Quantum Circuit Learning, Quantum Error Regression, Quantum Kernel Methods),four classical machine learning techniques (Lasso, Ridge, Random Forest, Gradient Boosting, Support Vector Regression), and Bayesian Structural Time Series— across two sample size regimes (n=30 and n=80) with five features. Outcome of the study revealed robust sample-size-dependent performance hierarchies in regularized linear methods (Lasso, Ridge) and Bayesian paradigms which ordinarily subsist in small-sample regimes of (n=30), with RMSE values of 4.46-5.74, while non-linear ensemble methods (Random Forest) exhibited superiority with moderate samples (n=80, RMSE: 2.07). Quantum machine learning methods had overtimes underperform classical benchmarks when exhibiting 91% higher error rates at small sample size of n=30, this may be due to classical method learned the noise, though Quantum Circuit Learning exhibited substantial convergence toward classical performance at n=80 (only 25% worse than best model),thus higher sample sizes thresholds will be better off for quantum-classical parity.
Quantum machine learning has emerged as a promising paradigm that leverages quantum computational principles to potentially outperform classical approaches on specific learning tasks. This paper presents a comprehensive empirical investigation comparing Quantum Machine Learning (QML), specifically Quantum Support Vector Machines (QSVM) against Classical Machine Learning (CML) baselines including Logistic Regression, K Nearest Neighbors and classical SVMs. We implement quantum kernel methods using variational quantum circuits with angle embedding, IQP and ZZ feature maps on datasets exhibiting varying structural complexity. Our experiments on synthetic quantum generated datasets (Quantum Parity, Quantum Entanglement, Quantum Interference) demonstrate that QSVM achieves superior classification accuracy with improvements ranging from 2.9 % to 60 % over the best classical baselines achieving a 55.6 % overall win rate. Notably, on the Quantum Parity dataset, QSVM consistently outperformed all classical models across multiple configurations. On real-world benchmark datasets (Breast Cancer, Iris, Wine), QSVM Angle achieved 88% accuracy on Breast Cancer compared to 76% for classical SVM Linear a 15.8 % relative improvement while matching the best classical performance on Iris(100%)and Wine(92%). All experiments were conducted using quantum circuit simulation on classical hardware. These results provide empirical evidence that quantum kernel methods offer meaningful advantages over classical approaches on datasets with complex feature interactions. We discuss the theoretical foundations of these improvements including quantum feature space expressivity and kernel alignment.
The forecasting of financial time series has gained more significance in decision making within a dynamic economic setting. Over the last few years, there has been a push in exploring both classical machine learning methods and novel quantum machine learning models with a view to enhance predictive accuracy. This paper suggests a quantum-classical regression framework developed that combines the feature selection in the form of a Random Forest in a hybrid approach, dimensionality reduction in the mode of Principal Component Analysis (PCA), and predicting in the form of a Variational Quantum Circuit (VQC). It is tested in various financial indicators, as BSE ESG, Carbon Exchange, Energy, Green Exchange, Oil and Gas and Power, with the help of RMSE and R 2 as the measure of performance. As experimental findings indicate, the classical algorithms like Random Forest and k-Nearest Neighbors always have the best accuracy and stability compared to quantum and hybrid ones. Quantum models are unstable, in contrast to Quantum kNN which is fairly stable. The hybrid model performs moderately with consistent error values but fairly lower explanatory power with significant results mostly on the BSE ESG data. In general, the paper has pointed out that classical approaches are still best in structured financial prediction tasks and hybrid quantum-classical models are potentially effective, but not yet competent. The results give valuable information on the existing limitation and future of the quantum machine learning to financial forecasting applications.
Recent advances in quantum machine learning (QML) offer new opportunities for chemical property prediction, yet their practical performance relative to established classical models remains poorly characterized on real-world datasets. Building on our previous benchmark of classical and deep learning models for collision cross-section (CCS) predictions, we present an empirical comparison of quantum kernel regression (QKR) and a variational quantum regressor (VQR) against classical machine learning (CML) techniques, including Random Forest (RF), support vector regression (SVR), Lasso, and a Voting Regressor (VR) ensemble. Using an aquatic dissolved organic matter (DOM) dataset with five molecular descriptors and five chemical classes, we systematically investigate QKR feature map repetitions and classical readout kernels, as well as VQR circuit depths and optimizer choices, to identify performance-optimal QML configurations. Regression performance is evaluated using the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R2) across training-set sizes up to 600 molecules per class. Overall, RF and Lasso deliver the most robust CCS predictions, achieving R2 ≥ 0.9 for lignins, carbohydrates, lipids, and proteins. Meanwhile, the optimized QKR architecture exhibits substantial gains as data increase and achieves competitive performance on chemically homogeneous subsets such as carbohydrates and lipids. In contrast, the VQR ansatz remains consistently weaker than both QKR and the classical baselines across all classes and data sizes. The results highlight the strong influence of dataset size, feature representation, and molecular heterogeneity on QML performance while also identifying conditions under which quantum methods may become competitive in future studies.
In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the variational quantum circuit and the quantum kernel estimator (QKE). We provide a first evaluation on the performance of these classifiers when using a hyperparameter search on six widely known and publicly available benchmark datasets and analyze how their performance varies with the number of samples on two artificially generated test classification datasets. As quantum machine learning is based on unitary transformations, this paper explores data structures and application fields that could be particularly suitable for quantum advantages. Hereby, this paper introduces a novel dataset based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. We further compared the performance of VQC and QKE on six widely applicable datasets to contextualize our results. Our results demonstrate that the VQC and QKE perform better than basic machine learning algorithms, such as advanced linear regression models (Ridge and Lasso). They do not match the accuracy and runtime performance of sophisticated modern boosting classifiers such as XGBoost, LightGBM, or CatBoost. Therefore, we conclude that while quantum machine learning algorithms have the potential to surpass classical machine learning methods in the future, especially when physical quantum infrastructure becomes widely available, they currently lag behind classical approaches. Our investigations also show that classical machine learning approaches have superior performance classifying datasets based on group structures, compared to quantum approaches that particularly use unitary processes. Furthermore, our findings highlight the significant impact of different quantum simulators, feature maps, and quantum circuits on the performance of the employed quantum estimators. This observation emphasizes the need for researchers to provide detailed explanations of their hyperparameter choices for quantum machine learning algorithms, as this aspect is currently overlooked in many studies within the field. To facilitate further research in this area and ensure the transparency of our study, we have made the complete code available in a linked GitHub repository.
In this paper, we present a reproducible benchmarking framework that systematically compares QML models with architecture-matched classical counterparts across three financial tasks: (i) directional return prediction on U.S. and Turkish equities, (ii) live-trading simulation with Quantum LSTMs versus classical LSTMs on the S\&P 500, and (iii) realized volatility forecasting using Quantum Support Vector Regression. By standardizing data splits, features, and evaluation metrics, our study provides a fair assessment of when current-generation QML models can match or exceed classical methods. Our results reveal that quantum approaches show performance gains when data structure and circuit design are well aligned. In directional classification, hybrid quantum neural networks surpass the parameter-matched ANN by \textbf{+3.8 AUC} and \textbf{+3.4 accuracy points} on \texttt{AAPL} stock and by \textbf{+4.9 AUC} and \textbf{+3.6 accuracy points} on Turkish stock \texttt{KCHOL}. In live trading, the QLSTM achieves higher risk-adjusted returns in \textbf{two of four} S\&P~500 regimes. For volatility forecasting, an angle-encoded QSVR attains the \textbf{lowest QLIKE} on \texttt{KCHOL} and remains within $\sim$0.02-0.04 QLIKE of the best classical kernels on \texttt{S\&P~500} and \texttt{AAPL}. Our benchmarking framework clearly identifies the scenarios where current QML architectures offer tangible improvements and where established classical methods continue to dominate.
The growing complexity, interdependencies, and rapid fluctuations inherent in modern financial markets create substantial challenges for accurate forecasting, portfolio optimization, and risk management. Conventional machine learning techniques, while powerful, often face limitations in capturing nonlinear relationships and processing high-dimensional datasets efficiently. Quantum machine learning (QML) has emerged as a promising paradigm that leverages quantum computing principles to enhance predictive modeling in finance. This study presents a comprehensive investigation into the application of QML methods—including variational quantum circuits, quantum kernel estimation, and quantum-enhanced support vector machines—for financial time-series prediction and asset price classification. We propose a hybrid quantum-classical framework that integrates quantum feature mapping with classical optimizers to improve model expressiveness and convergence. Empirical experiments are conducted using historical stock market data and synthetic datasets to benchmark QML approaches against established classical models such as long short-term memory networks and gradient boosting machines. The results demonstrate that QML techniques can achieve superior prediction accuracy and lower computational latency under certain data regimes, particularly when dealing with small-to-medium-sized datasets and high feature correlations. Additionally, the study examines scalability considerations, hardware constraints of near-term quantum devices, and the interpretability of quantum model outputs in financial decision-making contexts. The findings underscore the transformative potential of quantum machine learning as an innovative tool for advancing predictive analytics in finance and provide practical insights into how financial institutions can begin integrating QML capabilities into their workflows.